Novel Materials Laboratory

Department of Physics

Department of Chemistry

Division of Materials Science and Engineering

Angle Resolved Photoemission Spectroscopy

Hemispherical electron energy analyzer


EF = Fermi energy

Evac = Vacuum level

Ei , ki= initial energy and momentum of electron in solid

Ef , kf = final energy and momentum of electron following excitation

E, k = energy and momentum of free electron in vacuum after emission

F = Evac EF = work function

hn = incident photon energy


Energy conservation gives E(k) = hn F Ei(ki)

Momentum conservation parallel to the surface gives:







Momentum is not conserved perpendicular to the surface, but for a given inner potential V0, we can write:


By measuring the kinetic energy (E) and momentum (k) of the electron in vacuum, the dispersion of the electron state E(k) in the solid can be determined